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CSM51Asolution_chapter8

# Exercise 88 y0 y0 y0 x y2 0 1 0 1 0 0 0 0 0 0 1 0 1

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Unformatted text preview: 010 01 b 011 D 10 c E 100 101 F From the state table and the encoding we get the following K-maps. Exercise 8.8 y0 y0 y0 x Y2 : 0 1 0 1 0 0 0 0 0 0 1 0 1 0 0 y2 0 x Y1 : 0 0 1 0 0 1 1 1 1 0 0 0 0 1 1 y2 0 x Y0 : 1 1 1 1 0 0 0 0 0 0 1 y2 1 y0 0 1 1 1 0 1 y1 0 y2 0 y0 0 0 0 0 1 0 y1 0 y2 1 y1 x z1 : x z0 : y1 y1 The corresponding switching expressions are 0 Y0 = y0 00 0 0 Y1 = x0 y2 y1 y0 + x0y1y0 + xy2 y0 + xy1y0 0 000 Y2 = x0 y2 y0 + x0y1 y0 + xy2y0 + xy2 y1y0 z1 = y2y0 + xy0 0 0 z0 = x0y1y0 + y2 y0 + xy0 The sequential network is shown in Figure 8.8 on page 128. : Direct application of K-maps is not possible for this problem. To design this network it is important to decompose it into smaller parts, as shown in Figure 8.9. The NOTBCD module detects when the input code, or the stored minimum value is not a valid BCD code. The input vector is represented by the vector x = x3 ; x2 ; x1 ; x0 , and the state vector is y = y3 ; y2 ; y1 ; y0 . Input x y is not a valid BCD code if x 9 y 9. This condition is represented by the expression x is not BCD = x3 x2 + x3 x1 y is not BCD = y3 y2 + y3 y1 . The NOTBCD module is implemented by an expression that combines both cases: Exercise 8.9 NOTBCD = x is not BCD + y is not BCD = x3 x2 + x3 x1 + y3 y2 + y3 y1 128 x’ y2 y0’ x’ y1 y0 x y2 y0 x y2’ y1’ y0’ x’ y2’ y1’ y0 x’ y1 y0’ x y2 y0’ x y1 y0 Solutions Manual - Introduction to Digital Design - February 22, 1999 Y2 Y1 Y0 y0’ y2 y2’ y1 y1’ y0 y0’ CK y2 y0 x y0 x’ y1 y0 y2 y0’ x y0’ z1 z0 Figure 8.8: Sequential network for Exercise 8.8 The MIN module is speci ed as: Inputs: x; y 2 f0; 1; 2;    ; 15g Output: z 2 f0; 1; 2;    ; 15g Function: z = x if x y y otherwise The MIN module may be implemented as an iterative array, comparing bits from most-signi cant to least-signi cant. Each bit slice has two data" inputs xi and yi and two carry" inputs ei equal and si xj yj for some j i, and the outputs: mi , ei,1 , and si,1 . The folllowing expressions are used for each output: ei,1 = eixi  yi0...
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